A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Almost all maps are asymmetric
Journal of Combinatorial Theory Series B
Random sampling of large planar maps and convex polyhedra
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Linear-Time Succinct Encodings of Planar Graphs via Canonical Orderings
SIAM Journal on Discrete Mathematics
Enumeration of rooted planar triangulations with respect to diagonal flips
Journal of Combinatorial Theory Series A
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Progressive lossless compression of arbitrary simplicial complexes
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Fast General Methodology for Information-Theoretically Optimal Encodings of Graphs
SIAM Journal on Computing
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Random Sampling from Boltzmann Principles
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Regular Orientations, Arboricity, and Augmentation
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
On random planar graphs, the number of planar graphs and their triangulations
Journal of Combinatorial Theory Series B
A bijection for triangulations of a polygon with interior points and multiple edges
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Drawing planar graphs using the lmc-ordering
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal succinct representations of planar maps
Proceedings of the twenty-second annual symposium on Computational geometry
Early-split coding of triangle mesh connectivity
GI '06 Proceedings of Graphics Interface 2006
Streaming compression of triangle meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Selective decompression of vector maps
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Quick encoding of plane graphs in log 214 bits per edge
Information Processing Letters
Intervals in Catalan lattices and realizers of triangulations
Journal of Combinatorial Theory Series A
On the number of α-orientations
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
A compact encoding of plane triangulations with efficient query supports
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
Transversal structures on triangulations, with application to straight-line drawing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Planar graphs, via well-orderly maps and trees
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
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We present a bijection between the set of plane triangulations (aka. maximal planar graphs) and a simply defined subset of plane trees with two leaves per inner node. The construction takes advantage of the minimal realizer (or Schnyder tree decomposition) of a plane triangulation. This yields a simple interpretation of the formula for the number of plane triangulations with n vertices. Moreover the construction is simple enough to induce a linear random sampling algorithm, and an explicit information theory optimal encoding.